Deterministic Response Research Articles

Uncertainty quantification in the modal analysis of aircraft stiffeners: A Perturbation Technique approach in SFEM

Structural members, such as stiffeners, are crucial in aeronautical structures, providing essential dynamic stiffness. However, variability introduced by manufacturing and assembly processes, as well as material inconsistencies, can lead to uncertainties in structural performance. It is crucial to incorporate these uncertainties into structural analysis to ensure reliable design. This paper utilizes the Stochastic Finite Element Method (SFEM) to address uncertainties in typical structural members used in aeronautics. The Perturbation Technique, based on Taylor series expansions, was employed to model uncertainties in aircraft stiffeners. The study focuses on natural frequencies and modal analysis to evaluate the impact of uncertainties on beams with hat and Z sections, commonly used as stiffeners in aircraft panels. These stiffeners were modeled using the Timoshenko beam theory, and sensitivity analysis was performed to identify key contributors to variability. The perturbation parameter was validated through Monte Carlo simulations. Sensitivity analysis, employing gradient-based methods, identified significant factors affecting variability in natural frequencies. A different perturbation parameter was necessary based on the stiffener's geometry: thickness variations required a perturbation parameter on the order of 10−3, whereas dimensions changes in the flange and height required parameters on the order of 10−2. These results underscore the importance of choosing appropriate perturbation magnitudes to avoid inaccuracies in the deterministic frequency response. Once a perturbation parameter is established, it can be applied to similar regions, ensuring the robustness of the SFEM methodology in analyzing the dynamic response of aeronautical structural reinforcements.

Dynamic reliability assessment for high CFRDs incorporating ground motion and material parameter variability via GPDEM

The randomness of earthquake and material parameters significantly impacts the seismic response and dynamic reliability of geotechnical engineering structures. In this study, a dynamic reliability analysis method for high concrete face rockfill dams (CFRDs) under the influence of random factors is proposed by combining random sample generation methods with the generalized probability density evolution method (GPDEM). Firstly, the spectral representation-random function method is employed to achieve dimensionality reduction expression for intensity-frequency non-stationary ground motion. Sensitivity analysis is then used to identify the random variables of the rockfill constitutive model, and the improved generalized F-discrepancy (GF-discrepancy) method is utilized to generate random material parameters. Then, the random samples of earthquake and material parameter are introduced into the finite element calculation of CFRD, conducting a series of dynamic finite element calculations. Finally, GPDEM is used to derive probability information and dynamic reliability from the deterministic time history responses. The results indicate that random factors contribute to the variability of seismic response and dynamic reliability. Stochastic ground motion significantly affects extreme values, while variability in material parameters has a more pronounced influence on the overall process of seismic response. These findings provide valuable references for the seismic design of CFRDs.

Deterministic responses of biodiversity to climate change through exotic species invasions.

Biodiversity is increasingly threatened by local extinction under global climate change. This may reflect direct effects of climate on poorly adapted native species or increased impacts of exotic species in these conditions, but their relative importance is poorly understood. By examining global occurrence records of 142 plant species found in the Yangtze River Valley, we found that the climatic niches of exotic species differed from those of natives, mainly reflecting exotics being most common in warmer, drier and more isothermal climates in their native ranges. These differences in climatic niches, especially temperature, predicted invasion intensity in 459 plots along a 1,800-km transect in the Yangtze River Valley. On the basis of this strong match between model predictions and field survey results, we predict that invasions will probably be more intense in future climatic conditions, especially from warming at the coldest sites. The direct negative effect of warming on native diversity was larger than the indirect effects mediated through increased invasions. However, moderate invasion increased communities' overall species diversity. More broadly, our study highlights the role of exotic species in the ecological response of regional biodiversity to global climate change.

Transient Dynamic Response of Generally Shaped Arches under Interval Uncertainties

This paper endeavors to investigate the characteristics of the transient dynamic response of a generally shaped arch when influenced by uncertain parameters while being subjected to specific external excitation. The equations of motion of the generally shaped arches are derived by the differential quadrature (DQ) method, and the deterministic dynamic responses are calculated using the Newmark-β method. By employing the Chebyshev inclusive function, an interval method based on a non-intrusive polynomial surrogate model is developed, and the uncertain dynamic responses are reckoned by enabling numerical simulations. The results of the proposed interval method are compared with those obtained from the scanning method for validation. The effects of various shapes and rise span ratios on the dynamic responses are investigated through a parametric study. The results suggest that the degree of fluctuation in the uncertain dynamic behavior is influenced by the type of parameter. Additionally, the responses of each shaped arch decrease with the increase in the rise span ratios, and with the same rise span ratio, the deterministic responses and corresponding uncertain responses are also affected by the shape of the arch, and they are considered to be at a minimum when the arch shape is parabolic. This study will enhance understanding of the dynamic properties of arches with uncertainties and provide some basis for the assessment and health monitoring of arch structures.

Dynamic Wrinkling Instability of Elastic Films on Viscoelastic Substrates

Abstract The dynamic instability of stiff films on compliant substrates has received sustained attention due to the potential applications in flexible functional devices. Film/substrate system-based devices are increasingly utilized under dynamic conditions, including dynamic sensors, tunable optical components, anti-fouling surfaces, etc. To better design the dynamic characteristics of devices based on film/substrate systems, it is essential to establish a comprehensive dynamic model and find out the deterministic and non-deterministic instability domains of nonlinear dynamic wrinkling under time-varying biased loads. In this paper, a multi-level coupling time-varying parameter excitation dynamic model for films bonded on Kelvin viscoelastic substrates is developed. The damping effect on the nonlinear dynamic responses of wrinkled film/substrate systems under step, slope and biased sinusoidal axial time-varying excitations are analyzed. We revealed and analyze the nonlinear dynamic behavior of film/substrate systems, which are significantly influenced by the excitation frequency and viscous coefficients of substrates. Various response forms, such as excitation-following deterministic responses, chaotic responses, and double-period resonant responses, are observed. We analyzed the parametric excitation induced dynamic bifurcation of the time-varying energy barrier that causes the nonlinear dynamic phenomenon, and provided deterministic and non-deterministic dynamic response domains. Based on the theory and results, methods for generating responses of specific types are proposed, offering theoretical guidance for designing dynamic characteristics of devices based on film/substrate systems.

Analytical solution versus the Monte Carlo simulation for studying the H+ beam neutralization in H2 gas target neutralizer

A comparative Study on the conversion of an energetic H+ beam inside a cell neutralizer filled with hydrogen gas target is conducted by two different methods to determine the maximum beam neutralization efficiency and corresponding optimal gas thickness in terms of beam energy, ranging from 1 keV to 10 MeV. One method analytically solves the equations of particle flux with a deterministic response. The other uses the random collisional probability based on the Monte Carlo simulation with non-deterministic response, which is implemented by COMSOL software. Effective reactions of charge exchange and reionization are commonly considered in both methods with the energy-depended collisional cross section. The results obtained from the two methods are compared, demonstrating good fitness with a mean difference of ±1.5 %. This acceptive difference arises often due to statistical errors that occur in the Monte Carlo calculations. Additionally, a close agreement is found between calculated and measured efficiencies.

Analysis of geometric uncertainties in 3D thermo-fluid problems solved by RBF-FD meshless method

The tolerances of production processes can lead to uncertainties in the behaviour and in the features of the manufactured products. From the point of view of the design of engineering components it is therefore of valuable practical interest to be able to quantify such uncertainties as well as the expected, i.e., averaged, performances. Such uncertainty quantification is carried out in this work by means of the Non-Intrusive Polynomial Chaos (PC) method in order to estimate the propagation of geometrical uncertainties of the boundaries, i.e., when the boundaries are described by stochastic variables. Existing deterministic solvers can be used with the PC method because of its non-intrusive formulation, allowing an accurate and practical prediction of the random response through a simple set of deterministic response simulations. The Radial Basis Function Finite Differences (RBF-FD) method is employed as a black box solver for the computation of the required set of responses defined over deterministic boundaries. The RBF-FD method belongs to the class of meshless methods which do not require a computational mesh/grid, therefore its main capability is to easily deal with practical problems defined over complex-shaped domains. The geometrical flexibility of the RBF-FD method is even more advantageous when coupled to the Non-Intrusive PC method for uncertainty quantification since different deterministic solutions over different geometries are required. The applicability of the proposed approach to practical problems is presented through the prediction of geometric uncertainty effects for a steady-state forced convection problem in a 3D complex-shaped domain.

Skeletal muscle cells opto-stimulation by intramembrane molecular transducers

Optical stimulation and control of muscle cell contraction opens up a number of interesting applications in hybrid robotic and medicine. Here we show that recently designed molecular phototransducer can be used to stimulate C2C12 skeletal muscle cells, properly grown to exhibit collective behaviour. C2C12 is a skeletal muscle cell line that does not require animal sacrifice Furthermore, it is an ideal cell model for evaluating the phototransducer pacing ability due to its negligible spontaneous activity. We study the stimulation process and analyse the distribution of responses in multinuclear cells, in particular looking at the consistency between stimulus and contraction. Contractions are detected by using an imaging software for object recognition. We find a deterministic response to light stimuli, yet with a certain distribution of erratic behaviour that is quantified and correlated to light intensity or stimulation frequency. Finally, we compare our optical stimulation with electrical stimulation showing advantages of the optical approach, like the reduced cell stress.

Evaluating the Performance of Large Language Models in Hematopoietic Stem Cell Transplantation Decision Making

Introduction: Large Language Models (LLMs) are a form of Artificial Intelligence (AI), by identifying patterns and connections within data, they can predict the most likely words or phrases in specific contexts. Previous studies have indicated that GPT (Generative Pre-trained Transformer; OpenAI) performs well in answering single-choice clinical questions. However, its performance seems to be less satisfactory when dealing with multiple-choice questions and more intricate clinical cases (Cosima et al. 2023 EAO; Cascella et al. 2023 J Med Syst). Notably, no study has evaluated LLMs responses in the context of Transplantation Decision Making, a complex process heavily reliant on physician expertise. Additionally, most studies focused solely on GPT's performance, without considering other competitive LLMs like Llama-2 or VertexAI. Our study aims to assess the performance of LLMs in the domain of hematopoietic stem cell transplantation. Methods: We modified and anonymized the clinical histories of six hematological patients. An experienced hematologist reviewed and validated these modified clinical histories, which included demographic data, past medical history, hematology disease features (genetic data and MRD when available), treatment responses, adverse events from previous therapies, and potential donor information (related/unrelated, HLA, CMV status). We presented these clinical cases to six experienced bone marrow transplant physicians from two major JACIE accredited hospitals and 11 hematology residents from the University Milano-Bicocca. LLMs employed for the analysis were: GPT-4, VertexAI Palm 2, Llama-2 13b and 70b. LLMs were configured with different temperature settings to control token selection randomness, always maintaining low levels for more deterministic responses. A triple-blinded survey was conducted using Typeform, where both senior hematologists and residents provided anonymized responses with personal tokens. The senior hematologists, residents, and LLMs testers were unaware of the responses provided by the other groups. We calculated Fleiss K (K) and overall percentage of agreement (OA) between residents and LLMs, considering the consensus answer (CoA) among experts as the most frequent response. Subsequently, OA and K values for both residents and LLMs were compared using T- or Mann-Whitney tests with Graphpad v 10.0.1. Results: The results showed perfect agreement among experts in patient transplant eligibility assessment (K=1.0) and substantial agreement in the choice of donors and conditioning regimens (K=0.62 for both questions). Fair agreement was observed in Transplant Related Mortality (TRM) estimation (K=0.22). The median OA and K value between residents and the CoA of experts were 76.5% (range 52.9-88.2%) and 0.61 (range 0.4-0.8), respectively. The median OA and K value between LLMs answers and experts were 58.8% (range 47-71%) and 0.45 (range 0.3-0.61), respectively. The mean OA and K value of residents were significantly higher compared to LLMs (p=0.02). Specifically, residents showed higher median OA and K values in patient eligibility assessment (median OA 100 vs. 83% and K 1 vs. 0.78; p=0.01). However, there was no significant difference in median K for donor choice (0.56 vs. 0.56), conditioning regimen (0.67 vs. 0.33), and TRM evaluation (0.33 vs. 0) (Table 1). The median K values of GPT-4, Palm-2, Llama2-13b, and Llama2-70b were 0.49, 0.53, 0.33, and 0.53 respectively (Figure 1). Conclusion: Our study sheds light on the potential and limitations of LLMs in complex hematopoietic stem cell transplantation decision-making. While LLMs showed promising results with a median OA of 59%, residents demonstrated superior performance. LLMS displayed good performances in patients' eligibility and donor choice but showed shortcomings in conditioning regimens and TRM evaluation. Not using a rating scale from experts when evaluating LLMs responses aimed to avoid potential bias. However, it is important to note that the consensus answer, even though it was the most frequent, does not necessarily imply that other responses provided by the experts were incorrect. Therefore, the lower consensus among the experts in TRM evaluation, possibly due to the challenge of precisely calculating TRM in a survey-based evaluation, should also lead to a cautious approach when evaluating residents and LLMs answers in this setting.

Dynamic Responses of Train-Symmetry-Bridge System Considering Concrete Creep and the Creep-Induced Track Irregularity

This work considers the influence of concrete creep on track irregularities and establishes the dynamic motion equation of the train-track-bridge coupling system. The track irregularity is obtained by superposition of the initial geometric irregularity and additional geometric irregularity of the steel rail caused by creep. When high-speed railway trains pass through bridges; the vertical acceleration and vertical displacement of continuous beam bridges are related to the train’s operating speed, and the influence of creep camber is relatively small. At the same time, considering the randomness of track irregularities, the dynamic responses of the train track bridge coupling system under the action of random track irregularities are analyzed, and the dynamic responses of trains at different operating speeds are obtained. The deterministic and uncertain dynamic responses of the train track bridge system were compared and analyzed to verify the accuracy of the Karhunen Loéve expansion (KLE)-Point estimate method (PEM) calculation results. The results indicate that the random characteristics of track irregularities have a significant impact on train dynamic response. Based on the random system vibration analysis and considering the safety and comfort indicators of high-speed railway trains, the creep deformation limit of a continuous beam bridge with a length of 48 m + 80 m + 48 m is obtained to be 19 mm. This is the first time that the dynamic responses of train-symmetry-bridge system are calculated by considering concrete creep and the creep-induced track irregularity, which has certain significance for understanding the dynamics of train -bridge system. In addition, the proposed creep threshold is also of great significance to ensure the safety of traveling.

Carbon steel electrodes within chloride induced reinforcement corrosion in cracked concrete: Approximation to deterministic system response

AbstractResearch on chloride‐induced corrosion in cracked, reinforced concrete is of steady economic and scientific importance. The ever‐growing amount of reinforced concrete structures in need for maintenance and preservation calls for suitable and reliable methods to assess the current state. The present study demonstrates a specimen design that allows authentic corrosion monitoring, including solely carbon mild steel as working and counter electrodes, singularly cracked concrete as electrolytes and a conservative dismantling of the anodic steel‐concrete interface (SCI) at the end of 180 days of monitoring. The electrochemical features of the evolved specimen narrow down to the textbook behavior of the investigated electrodes according to the electro potential series of metals. The most prominent results are the chloride profiles at depth of rebar along the SCI, the build‐up of driving potential, and the decisive contribution arising from the anodic equilibrium potential. Accordingly, future repair methods should always include observation of the anodic equilibrium potential and their effectiveness is clearly addressed in the course of that value.

Reliability-constrained optimal attitude-vibration control for rigid-flexible coupling satellite using interval dimension-wise analysis

This study proposes an uncertain optimal attitude–vibration control method for rigid–flexible coupling satellites with reliability constraints based on the interval dimension-wise analysis. To model the complex uncertain control system, multi–source uncertainties in rigid–flexible coupling satellites are quantified to interval parameters. Based on the nominal rigid–flexible coupling satellite dynamic model, the interval attitude–vibration model is derived and the corresponding coupled state equation is established. Considering polynomial chaos expansions in the surrogate model, an interval dimension-wise analysis (IDWA) method is proposed to predict the uncertain state response of the uncertain attitude–vibration control system, which can help solve the overestimation problem of the conventional perturbation method. An interval linear quadratic regulator (LQR) is proposed by combining the IDWA method and deterministic LQR, to accurately optimize the uncertain control input and cost function. With regard to harsh deterministic state response constraints, this study proposes a non-probabilistic time-dependent reliability method, which allows for an effective evaluation by flexibly characterizing the relationship between the uncertain state response and threshold. The reliability-constrained multi–objective optimal attitude–vibration control problem can be solved by considering the nominal cost function and uncertain state response as two optimization objectives. The effectiveness of the proposed method is verified using a rigid–flexible coupling satellite.

Graphene Quantum Dots for Multifaceted Diagnostics

Due to their unique physical and electronic properties as well as high biocompatibility and water solubility, functionalized graphene quantum dots (GQDs) have found utilization in a variety of biomedical applications. GQDs can serve as carriers for drugs and genes while tracing their delivery pathways in vitro and in vivo with their visible and near-infrared fluorescence. In addition to therapeutic applications, our recent work explores diagnostic modalities of these novel nanomaterials. GQDs synthesized bottom-up form a single glucosamine precursor, or top-down from reduced graphene oxide can serve as nanoscale temperature sensors for biological processes. They exhibit linear and reversible visible/NIR fluorescence quenching by up to 19.3 % in suspension with temperature increase form 25 to 49 ⁰C. A more pronounced trend is observed in HeLa cells with over 40% quenching in that temperature range. Our findings suggest that such deterministic response can serve as non-invasive reversible/photostable mechanism for temperature sensing in microscopic subcellular biological environments. Another diagnostic modality of GQDs involves their capability for magnetic resonance imaging. When doped with Mn2+ ions during their bottom-up synthesis, GQDs exhibit substantial r₂/r₁ relaxation parameter ratios of 11.19, showing potential as dual-mode T1 or T2 contrast agents. Their Gd3+-doped counterparts possess r₂/r₁ ratios of 1.148 with high r1 of 9.546 mM-1s-1 compared to commercial contrast agents, suggesting their utilization as T1 contrast agents. Given that doping did not affect their biocompatibility or fluorescence properties, such doped GQDs can serve as multimodal MR and fluorescence imaging agents. Metal-doped GQDs possess the capability ultrasonic contrast imaging that can be utilized for higher precision and deeper tissue diagnostic applications. They demonstrate high-contrast properties in ultrasound brightness mode by a factor of 10 surpassing undoped GQD structures. The successful imaging enhancement was observed in tissue phantom and animal tissue, suggesting that GQDs can be tracked by ultrasound imaging and used as contrast agents for the improvement of the deterministic power of this widely available imaging approach. GQD intrinsic fluorescence can itself serve as a non-invasive diagnostic sensing tool, as it can be affected by the binding of different drugs, genes and biomolecules to the GQDs. This optical sensing mechanism is used in our work for identifying trace quantities of cancer-generated genes for early personalized cancer detection. The sensor is prepared from GQDs complexed with the bait DNA sequence complementary to the target pancreatic cancer miRNA. It effectively discriminates between complementary single-stranded DNA sequences and random control genes with the sensitivity in the nanomolar range. Cancer gene detection is further verified by identifying both, the stem and the loop portions of the pancreatic cancer-generated pre-miR-132. Given the success of these different diagnostic applications, GQDs can be considered a highly perspective theragnostic tool for a variety of disease targets.

Random Dynamic Analysis and Running Safety Assessment of Long-Span Cable-Stayed Bridge Under High-Speed Trains Subjected to Earthquake Excitations and Track Irregularities

Running trains on a long-span bridge under earthquake is an inevitable problem for the high-speed railway in seismic regions. This paper aims to investigate the seismically random dynamic behavior of train–cable stayed bridges interaction system using the probability density evolution method (PDEM). The system simultaneously involves the multi-effect of random multi-point earthquake excitations with traveling waves and random track irregularity. The multi-point earthquake excitations, composed of lateral and vertical positions, are generated by stochastic harmful functions (SHFs) and uniformly modulated into nonstationary random processes. The motion equation of such a system is established by coupling the 38-degree vehicles and bridges through the refined random wheel/rail contact relationship and accounting for the phase-lags of seismic travelling waves between pier excitations. PDEM is proven to be applicable to such time-dependent systems and is then used to transform the random excitations into a series of deterministic representative excitations with initial probability. By solving for the corresponding deterministic probability responses, various nonstationary random responses, including the time-dependent probability density evolution functions of random responses, mean values curves and standard deviations, can be obtained easily. A case study based on the cable-stayed bridge is then presented, and the results show the effectiveness and accuracy of the proposed method by comparison with Monte Carlo Simulation. Additionally, the influence of train speed and seismic intensity on the safety and reliability of trains is discussed.

Generalized probabilistic response surfaces for the buckling strength assessment of stiffened panels

The ultimate compressive strength of stiffened panels has been well studied and a variety of simplified buckling formulas are available. However, there is a significant degree of uncertainty that is associated with the parameters that affect the buckling problem and are currently not accommodated within the deterministic response surfaces. This work proposes a computationally efficient framework that is based on probabilistic methods, experimental design and inferential statistics for the construction of generalized buckling response surfaces that are founded on an acceptable risk level defined by the user. The process is demonstrated on a marine stiffened panel that includes “T” stiffeners. Finite Element models have been employed as the mapping function between the uncertain input variables and the response quantity. It is shown that surrogate modeling could not be used to accelerate the problem and therefore a limited number of computationally demanding simulations combined with formal statistical theory may be efficiently used. The constructed response fronts are associated with a probability of non-exceedance and may be further used within a reliability-based analysis and design scheme.

Stochastic Performance of Journal Bearing With Two-Layered Porous Bush—A Machine Learning Approach

Abstract This investigation presents the deterministic and stochastic responses of the journal bearing with a two-layered porous bush. Pressure equations in the porous layers and modified Reynolds equations in the clearance region are governed by the finite difference method (FDM). Stochastic analysis based on Monte Carlo simulation (MCS) is used to investigate the effect of random variation in input parameters caused by uncertain operating conditions, improper installations, and manufacturing imperfections. In order to enhance computational efficiency, this probabilistic study is conducted in conjunction with the machine learning (ML) model based on the support vector machine (SVM) algorithm. The uncertainty in the bearing responses is presented in the form of the probability density function (PDF), considering both the independent and combined effect of the stochastically varied input parameters. Graphical illustration of the data-driven sensitivity represents the relative significance of each input parameter affecting the steady-state responses of the journal bearing with two-layered porous bush. The findings of the present study reveal that the stochastic variations in the input parameters have a profound influence on the operational characteristics of the porous bearing. The outcome of the present study will be helpful in deciding the operational regime of the porous bearing under the practically relevant stochastic environment.

Predicting Deposition Rate and Closing the Loop on Aerosol Jet Printing with In‐Line Light Scattering Measurements

Aerosol jet printing is a compelling noncontact, digital manufacturing technology for flexible, hybrid, and conformal electronics, but batch‐to‐batch variability and process drift inhibit systematic study and translation to production environments. Emerging measurement techniques for the aerosol volume fraction, a key parameter governing deposition rate, have shown promise for real‐time response, including a recent demonstration of human‐in‐the‐loop control. By integrating improved light scattering measurements with custom software, a robust environment for real‐time monitoring is established and fully automated closed‐loop control over the deposition rate during printing is enabled. The physical basis for scattering measurements as a feedback source is examined and the quantitative insight this provides for ink development and fundamental process studies is highlighted. Three candidate process variables for closed‐loop control, namely the atomizer voltage, carrier gas flow rate, and print speed, are then evaluated. The atomizer voltage demonstrates the best extended duration validity because it addresses atomization variability directly, but carrier gas flow rate and print speed provide faster and more deterministic responses. This methodology is then demonstrated for electrical properties using a silver nanoparticle ink, maintaining 98% of printed patterns within 10% of the mean resistance value over 3 h of printing.

Probability Distributions of Asphalt Pavement Responses and Performance under Random Moving Loads and Pavement Temperature

Asphalt pavements are damaged by traffic load repetitions. Conventionally, the allowed number of load repetitions until pavement failure is calculated based on empirical transfer functions from deterministic pavement mechanical responses to performance. However, the mechanical responses and damage to the pavement are uncertain under a random realistic traffic load and pavement temperature. Therefore, the non-deterministic problem—that is, the probability distributions of asphalt pavement responses and performance under random moving loads and pavement temperatures—was investigated in this study. Random factors include the load pressure, vehicle wandering, speed, and temperature inside the asphalt layer. A combination of the response surface and first-order reliability methodologies was recommended to calculate the probability of mechanical responses at any point within the pavement, for reasons of computational efficiency. The accuracy of this method was verified by a Monte-Carlo simulation. Then, the effects of the mean values and standard deviations of the random factors on the probability distributions of the mechanical responses were discussed. Finally, probability distributions of pavement performance (i.e., probability density distributions of cumulative damage for fatigue failure and rutting after repeated random loads) were calculated using transfer functions and the probability distributions of the mechanical responses; thereby, the failure probability of the pavement after a given number of load repetitions was obtained. The results show that the previous deterministic analysis could not fully reflect the random characteristics of pavement mechanical responses under realistic random moving loads, and the mean values and standard deviations of the random factors have significant effects on the probability distributions of mechanical responses and performance. The failure probability of the pavement after a given number of load repetitions can be used as a guide to reliability-based pavement design. This study on the probability distributions of asphalt pavement responses and performance exhibits the potential to understand pavement behavior and could be beneficial as a complement during reliability-based pavement design.

Enabling Durable Ultralow-k Capacitors with Enhanced Breakdown Strength in Density-Variant Nanolattices.

Ultralow-k materials used in high voltage devices require mechanical resilience and electrical and dielectric stability even when subjected to mechanical loads. Existing devices with organic polymers suffer from low thermal and mechanical stability while those with inorganic porous structures struggle with poor mechanical integrity. Recently, 3D hollow-beam nanolattices have emerged as promising candidates that satisfy these requirements. However, their properties are maintained for only five stress cycles at strains below 25%. Here,wedemonstrate that alumina nanolattices with different relative density distributions across their height elicit a deterministic mechanical response concomitant with a 1.5-3.3 times higher electrical breakdown strength than nanolattices with uniform density. These density-variant nanolattices exhibit an ultralow-k of ≈1.2, accompanied by complete electric and dielectric stability and mechanical recoverability over 100 cyclic compressions to 62.5% strain.Weexplain the enhanced insulation and long-term cyclical stability by the bi-phase deformation where the lower-density region protects the higher-density region as it is compressed before the higher-density region, allowing to simultaneously possess high strength and ductility like composites. This study highlights the superior electrical performance of the bi-phase nanolattice with a single interface in providing stable conduction and maximum breakdown strength.

Non-stationary response of nonlinear systems with singular parameter matrices subject to combined deterministic and stochastic excitation

A new technique is proposed for determining the response of multi-degree-of-freedom nonlinear systems with singular parameter matrices subject to combined deterministic and non-stationary stochastic excitation. Singular matrices in the governing equations of motion potentially account for the presence of constraints equations in the system. Further, they also appear when a redundant coordinates modeling is adopted to derive the equations of motion of complex multi-body systems. In this regard, the system response is decomposed into a deterministic and a stochastic component corresponding to the two components of the excitation. Then, two sets of differential equations are formulated and solved simultaneously to compute the system response. The first set pertains to the deterministic response component, whereas the second one pertains to the stochastic component of the response. The latter is derived by utilizing the generalized statistical linearization method for systems with singular matrices, while a formula for determining the time-dependent equivalent elements of the generalized statistical linearization methodology is also derived. The efficiency of the proposed technique is demonstrated by pertinent numerical examples. Specifically, a vibration energy harvesting device subject to combined deterministic and modulated white noise excitation and a structural nonlinear system with singular parameter matrices subject to combined deterministic and modulated white and colored noise excitations are considered.